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Nearly half of Massachusetts voters would support the legalization of marijuana, according to a new Boston Globe poll that suggests the state could be fertile ground for a ballot campaign to legalize the drug here in 2016.

Forty-eight percent of likely voters said they would support a ballot question making it legal for adults over 21 to consume or possess limited amounts of marijuana, while 47 percent said they would oppose such a measure. Five percent said they do not know how they would vote.

The results indicate that support for legalization has moved from the political fringes only a few years ago into the mainstream, particularly among younger voters, baby boomers, and Democrats. However, many older voters, independents, and Republicans remain opposed to casual use of the drug.

The growing public acceptance of the drug has also been captured in national surveys that show that while Americans strongly opposed the legalization of marijuana from the 1970s through the late 1990s, they have recently come to support such efforts by a slim majority.

Advocates are trying to place a legalization measure on the ballot in Massachusetts and five other states in 2016, hoping to build on the passage of similar ballot questions in Colorado and Washington in 2012.

Marijuana supporters have targeted Massachusetts because voters here strongly approved measures that decriminalized possession of small amounts of the drug in 2008 and allowed its use for medical purposes in 2012.

“I don’t want to underestimate the value of a good campaign on either side,” which could shift public support for legalization in either direction, said John Della Volpe, chief executive of SocialSphere Inc., which conducted the poll for the Globe. But the results suggest, “You’ve got a trend toward acceptance, and this bodes pretty well for the proponents.”

‘I believe in marijuana if it’s given by a doctor to help people who are sick, but just to go ahead and use it? No.’

The live telephone survey of 601 likely voters was conducted from June 22 to June 24 and from June 29 to July 1. The margin of error was plus or minus 4 percentage points for the survey overall and 5.1 percentage points for a narrower sample of likely Democratic primary voters.

Robert Ayer, a 32-year-old pizzeria manager from Tewksbury, was among the respondents who said he would support the legalization of marijuana if the question were on the ballot.

“I think it would be good for our economy, for starters, and it’s no more harmful than alcohol or anything, so it wouldn’t really be a drag on society like everyone makes it out to be,” he said in a folllow-up interview. “Colorado is showing it really works.”

But like many older voters, Mary Ann Couch, a 68-year-old retired gas company worker from Springfield, said she opposes making the drug legal for casual use.

“I believe in marijuana if it’s given by a doctor to help people who are sick, but just to go ahead and use it? No,” she said in an interview. “You start with marijuana and go on to something else, and pretty soon you’re addicted.”

Yet the poll indicated that legalization would not encourage more people to use the drug.

If marijuana were legal, 10 percent of likely voters said they would definitely or probably use it — about equal to the 9 percent who said they currently use it, either regularly (4 percent) or once in the past year (5 percent). Thirty-five percent of those surveyed said they had used the drug, but not in the last year, while 49 percent said they had never used it.

The social stigma around the drug may also be lifting, according to the poll.

Seventy-eight percent of respondents said their perception of a friend would not change, either positively or negatively, if they learned that person used marijuana recreationally. Notably, that result was the same for older and younger voters, who were divided on other marijuana-related questions.

The poll found some concerns that the state’s current medical marijuana law may be too lenient. The regulations allow patients to purchase up to 10 ounces of marijuana every 60 days if a doctor deems it medically necessary. This amounts to approximately 500 joints over two months, and has led some physician groups to worry that the drug could be sold on the black market.

Forty-seven percent of respondents said they agreed that the 10-ounce limit is excessive, while 36 percent said it was appropriate and 17 percent said they did not know.

As it does each week, the Globe poll also tracked the candidates in the governor’s race.

Results showed that the Democratic primary contest is holding steady, with Attorney General Martha Coakley continuing to dominate her rivals: state Treasurer Steve Grossman and former federal health care official Don Berwick.

For the third straight week since the party convention in Worcester, Coakley had the support of 52 percent of likely Democratic primary voters.

Grossman was at 19 percent in the poll this week as well as last week, and at 18 percent three weeks ago. Berwick was at 8 percent this week and last week and 7 percent the week before that. The results show that neither Grossman, who won the convention, nor Berwick, who narrowly missed beating Coakley, has been able to use those strong showings to eat into Coakley’s lead.

In a general election, Coakley remains the only Democrat who would beat Republican Charlie Baker, although her lead has slipped slightly. She would top Baker 40 percent to 31 percent — a 9-point margin, down slightly from 11 points last week and 13 points the week before that.

Coakley’s drop came as she was dealt two separate blows — first as the state’s Supreme Judicial Court overruled her by allowing a casino repeal to go before voters, and then as the Supreme Court struck down a law she had defended that barred protesters within 35 feet of abortion clinics.